Simplify the following expression and state the condition under which the simplification is valid: $x = \dfrac{y^2 - 5y - 36}{y^2 + 4y}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{y^2 - 5y - 36}{y^2 + 4y} = \dfrac{(y - 9)(y + 4)}{(y)(y + 4)} $ Notice that the term $(y + 4)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(y + 4)$ gives: $x = \dfrac{y - 9}{y}$ Since we divided by $(y + 4)$, $y \neq -4$. $x = \dfrac{y - 9}{y}; \space y \neq -4$